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### Problem Overview:
The table shows the amounts of milk \( m \) (in cups) and flour \( f \) (in cups) needed to make a mix for biscuits. You are tasked with:
- Completing the table (part a).
- Describing the relationship between milk and flour (part b).
- Finding the constant of proportionality (part c).
- Writing an equation to relate the two quantities (part d).

### Part A: Complete the Table

The table currently looks like this:

| Milk \( m \) (cups) | Flour \( f \) (cups) | Total Mix \( t \) (cups) |
|---------------------|----------------------|--------------------------|
| 1.5                 | 3.0                  |                          |
| 5.83                | 8.75                 |                          |
| \( 2 \frac{1}{2} \) | \( 6 \frac{1}{4} \)  | 7                        |

Notice that the amount of flour is exactly twice the amount of milk in all rows. We can use this proportionality to fill out the total mix.

To find the missing entries for the total mix:
- For the first row, the total mix would be \( 1.5 + 3 = 4.5 \) cups.
- For the second row, \( 5.83 + 8.75 = 14.58 \) cups.
- The third row is already filled out as \( 7 \) cups.

### Updated Table:

| Milk \( m \) (cups) | Flour \( f \) (cups) | Total Mix \( t \) (cups) |
|---------------------|----------------------|--------------------------|
| 1.5                 | 3.0                  | 4.5                      |
| 5.83                | 8.75                 | 14.58                    |
| \( 2 \frac{1}{2} \) | \( 6 \frac{1}{4} \)  | 7                        |

### Part B: Proportional Relationship
Two quantities are in a proportional relationship if one quantity is a constant multiple of the other. Here, the relationship between the amount of flour and the amount of milk is proportional.

- The amount of flour \( f \) is always twice the amount of milk \( m \).
- So, the proportional relationship is between the milk and flour, where the ratio \( \frac{f}{m} = 2 \).

### Part C: Constant of Proportionality
The constant of proportionality \( k \) in this context is the factor by which you multiply the amount of milk to get the amount of flour.

- From the table, we observe that \( \frac{f}{m} = 2 \).
- Therefore, \( k = 2 \), meaning the flour is twice the milk.

### Part D: Equation Relating the Two Quantities
Using the constant of proportionality \( k = 2 \), we can express the relationship between milk and flour as an equation:

\[ f = 2m \]

This equation shows that the amount of flour \( f \) is twice the amount of milk \( m \).

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Would you like further clarification on any part of this problem? Here are five additional questions to deepen your understanding:

1. How would the table change if the relationship were \( f = 3m \) instead of \( f = 2m \)?
2. What would happen to the total mix if the amount of milk doubled in each case?
3. Can you think of another real-life example where two quantities are in a proportional relationship?
4. How would the equation change if the flour were half the amount of milk instead of double?
5. If you increase both milk and flour by the same proportional amount, how does that affect the total mix?

**Tip:** When solving proportionality problems, always check if the ratio between two quantities remains constant across all data points.

The table shows the amounts of milk and flour needed to make a mix for biscuits. Complete the table, describe the proportional relationship, find the constant of proportionality, and write an equation that relates the two quantities.

Explore the relationship between milk and flour in a biscuit mix. Learn to complete the table, describe proportional relationships, find the constant of proportionality, and write an equation for the quantities. Suitable for Grade 7 students.

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